Estimating the Magnitudes of Peak Streamflows
Peak streamflows documented in this study were determined at 32 USGS streamgages (fig. 3) by use of the rating curve (the relation between streamgage height and flow) for each station. Rating curves at streamgages are developed by relating gage height to streamflow for a range of flows. Streamflow data points used to develop a rating are determined most commonly by direct measurement at the streamgage (Rantz and others, 1982); or, if it is not possible to make a direct measurement, by indirect methods (Benson and Dalrymple, 1967). The rating curve is interpolated between measured streamflow data points and can be extrapolated beyond the highest streamflow data point; however, excessive extrapolation of the rating at high gage heights can result in large errors in streamflow (Rantz and others, 1982). Peak gage heights were obtained either from electronic data recorders or from surveyed high-water marks where recorders or stage sensors malfunctioned or were not available. The rating curve was used to compute peak streamflow from peak gage height. Direct streamflow measurements or streamflows determined by indirect methods served as recent data points for rating-curve verification and extrapolation. Flood-peak gage heights and streamflows were checked by USGS hydrologic technicians and determined to be correct as of October 2008.
Peak gage heights and streamflows were estimated for three ungaged sites through a variety of indirect methods, chosen on the basis of site conditions and available historical data. The three ungaged sites were the Baraboo River at Reedsburg, the Baraboo River at Rock Springs, and the Kickapoo River at Gays Mills. The Baraboo River at Rock Springs and Kickapoo River at Gays Mills are National Weather Service Peak Advanced Hydrologic Prediction Service automated and manual sites (http://www.crh.noaa.gov/ahps2/index.php?wfo=arx) for which there are gage-height data but no streamflow data (fig. 3).
Peak streamflow for the Baraboo River at Rock Springs was estimated through the use of the slope-area method (Dalrymple and Benson, 1967). In the slope-area method, streamflow is computed on the basis of a uniform-flow equation involving channel characteristics, water-surface profiles, and a roughness coefficient (Rantz and others, 1982). Computations were done with the USGS Slope Area Computation program (SAC) (Fulford, 1994) and surveyed channel geometry and high-water-mark data. An available HEC-RAS step-backwater hydraulic model for the Baraboo River was obtained from Robert Watson (National Flood Insurance Coordinator, Wisconsin Department of Natural Resources, written commun., 2008) and was used to determine the streamflow that yielded a profile that best matched the actual flood water-surface profile (Davidian, 1984).
For Rock Springs, the selected model-generated profile was within ±0.2 ft of high-water marks defining the actual flood profile. This provided an independent estimate of peak streamflow for comparison with the streamflow computed with the slope-area method.
In Reedsburg, no suitable stream reach was available to reliably employ the slope-area method, nor were there other suitable hydraulic features, such as a bridge contraction, that would allow employment of the contracted-opening method. An available HEC-RAS model was employed with various streamflows to generate water-surface profiles for comparison with the actual flood profile. The modeled streamflow that generated the profile that best matched the actual flood profile was selected for the peak-streamflow estimate. For Reedsburg, the peak flow was estimated to be within a range of discharge such that profiles determined by the low and high ends of the range were within 0.3 ft high water marks defining the actual peak flood flow.
For the Kickapoo River at Gays Mills, peak streamflow was estimated from rating extrapolation of USGS high-water marks and NWS flood-forecasting-station gage heights with historical stage-discharge measurements for the discontinued USGS streamgage in Gays Mills. The rating extrapolation was based on a log-based regression of historical floods greater than 5,000 ft3/s in 1961, 1965, 1966, and 1978. The rating extrapolation also was done for the August 2007 flood based on NWS flood-forecasting-station gage heights (Michael A. Welvaert, National Weather Service, La Crosse, Wis., written commun., 2008). In addition, Robert Watson (National Flood Insurance Coordinator, Wisconsin Department of Natural Resources, Madison, Wis.) ran an available step-backwater model for the Kickapoo River reach near Gays Mills to estimate the peak streamflow. The estimate was the modeled discharge that generated a water-surface profile best matching the actual flood profile based on the USGS high-water-mark elevations. Gage heights were referenced to NAVD 88 datum based on surveys of the streamgage-reference marks during the high-water-mark surveying.
Calculating Flood Probabilities of Peak Streamflows
The flood probability for a particular streamflow is the probability or odds of that streamflow being equaled or exceeded in any given year. For example, a probability of 0.01 means there is a 1 percent chance of that flow magnitude being equaled or exceeded in any given year. Stated another way, the odds are 1 in 100 that flow will equal or exceed that magnitude in any given year. The traditional concept of recurrence interval is directly related to the flood probability. By definition, the recurrence interval corresponding to a particular flood probability is equal to one divided by the flood probability. For example, the flood probability of 0.01 corresponds to the 100-year flood.
Flood probabilities associated with the peak streamflows for streamgages and three ungaged locations were estimated to indicate the relative magnitude of the June 2008 flooding. Discharges for selected flood probabilities (0.20, 0.10, 0.04, 0.02, 0.01, 0.005, and 0.002) were estimated using the procedure recommended by the Interagency Advisory Committee on Water Data (1982), commonly called the Bulletin 17B procedure. Users of this procedure calculate flood probabilities by fitting systematic annual-peak-discharge data to a log-Pearson type III (LPIII) distribution. The population properties of the LPIII distribution are determined from the streamgage annual peak-flow data, which results in uncertainty in the estimates of the flood probabilities. The uncertainty is a function of the sample size, the accuracy of the streamgage record, and how well the LPIII distribution fits the underlying data. If two independent estimates of flood probability are available, a properly weighted estimate will have a lower uncertainty than either independent estimate (Interagency Advisory Committee on Water Data, 1982). As such, the method outlined in Bulletin 17B appendix 8 was used where possible to achieve lower uncertainty in the estimate. The weights were computed as the inverse of the respective variances of the two independent estimates.
In Wisconsin, the second independent estimate for each rural streamgage site was obtained by use of regional regression equations for rural conditions (Walker and others, 2003). For some streamgages, estimates of basin characteristics were determined by use of geographic information system (GIS) techniques, which differ slightly from the methods used to develop the regression equations (Walker and others, 2003); these cases are noted in table 3. In some cases, the regional regression equations were not applied because the streamgages were in urban areas or had regulated streamflows. For those sites without a valid second independent estimate for the flood probabilities, the Bulletin 17B estimates were used directly, with no weighting method applied.
Estimates of discharge for the selected flood probabilities can then be used to estimate the range of flood probabilities of a particular flood by means of two approaches. The upper and lower bounds for the range of probability are determined by comparing a particular flood peak (in this case, the peak from the 2008 flood) directly to estimated flood peaks for the selected probabilities. This method fails to consider the uncertainty of the estimates of flood peaks for the selected probabilities. An alternative approach is to determine the 95-percent confidence intervals for flood peaks corresponding to each of the selected probabilities and to compare the particular flood peak to these confidence intervals. If the flood peak falls within a particular confidence interval for a given probability, that probability is considered to be a likely estimate for that peak. In cases where the flood peak falls within the confidence interval for multiple probabilities, the estimated flood probability is reported as a range.
Collection of High-Water-Mark Data
High-water marks were identified and flagged by the USGS in nine communities in southern Wisconsin during August 4–28, 2008, approximately 2 months after floodwaters receded. High-water marks were set on both sides of each stream at spacing of approximately 500 to 1,000 ft, in accordance with standard USGS methods (Benson and Dalrymple, 1967). Commonly, stain lines on buildings, trees, or other structures were used. High-water marks were readily visible within the flooded areas despite the 2 months between flooding and high-water-mark identification (fig. 4). High-water marks were identified, mapped, and photographed, and associated information was recorded. The quality of the high-water marks was subjectively rated in the field as excellent, good, fair, or poor by the high-water-mark crews. Ratings were based on the clarity of the mark and visual or hand-level comparison to nearby marks. Data collected during marking were tabulated into a database. A subset of high-water marks previously surveyed by Jefferson County, the city of Reedsburg, city of Janesville, and the U.S. Army Corps of Engineers was used to supplement and verify USGS high-water marks and expand the spatial coverage for the inundation maps.
High-water marks were surveyed within a few days after marking with a combination of surveying techniques. Primarily, a Real Time Kinematic Global Positioning System (RTK-GPS) was used to survey each high-water mark. Quality-assurance procedures included setting up the RTK-GPS base station at a high location (roof of hospital, municipal building, on the valley side, and so forth) for maximum satellite reception and radio coverage and locating a minimum of two control points with multiple repeated readings (Vertical Second Order Class I; preferred). The preferred method of surveying a high-water mark was to simply set the GPS rover on the high-water mark and collect fixed-point data. If the high-water mark was too high above the ground or if tree cover or building interference would not allow a fixed solution, GPS data for an intermediate survey point were collected a short distance away. The difference in elevation between the intermediate survey point and the desired high-water mark was measured using a hand level or an auto-level and surveying rod. This difference was then used to adjust the surveyed intermediate elevation to the actual high-water-mark elevation during post-processing. The high-water marks were surveyed to an expected accuracy of 0.1 ft. The datum used was the North American Vertical Datum of 1988 (NAVD 88). When the community was being surveyed over multiple days with multiple setups, a procedure was used that required surveying overlapping points (at least one control point and a few high-water marks) from multiple survey setups so that elevations could be double-checked and the accuracy between the surveys established. If a community survey included deviations from the quality-assurance plan, an additional survey was done to verify the accuracy across and within individual surveys.
Flood-peak inundation maps for the June 2008 flood were produced by use of GIS software and associated programs (Morlock and others, 2008). These maps show the maximum extent of floodwaters in and around each selected community. GIS layers of the high-water marks were generated from the survey data, overlain with the best digital-elevation-model (DEM) data available for each community, and superimposed on the corresponding National Agricultural Imagery Program 2006 air photo (U.S. Department of Agriculture, 2006) (table 1). The maps were checked by the USGS surveying and high-water-mark crews, and the high-water marks were compared spatially to check for mathematical or other errors. If a data point was still too high or too low when compared to neighboring points, the point in question was removed from the inundation mapping.
GIS Arc Macro Language (AML) programs were written to produce a plane representing the flood-peak water surface, which was fit through the high-water marks and sloped in the direction of water flow (Leslie Arihood, USGS Indiana Water Science Center, written commun., August 2008). Elevations between high-water marks are proportional interpolations of the high-water-mark data. A TIN (triangular irregular network) surface was fit through the data points, forming the estimated flood surface. A flood-depth map was made by subtracting the DEM of the land surface from the flood-peak water surface. The flood-peak inundated area TIN models were exported in a GIS file format (shapefiles) that delineates flood-peak extent.
After the elevation of the flood peak was determined and checked, flood-peak elevations from five streamgages in the communities were compared to surveyed high-water marks. The high-water-mark crews located a high-water mark directly on the streamgage house or nearby. The survey crews surveyed the reference marks at the streamgages along with the high-water marks to allow the arbitrary gage height to be shifted to match the survey data. This method served as an independent check of the flood-peak elevations in those communities.
Draft maps of the modeled flood-peak extent were sent to a contact in each community as an outside check of the model. Typically, the city engineer or public works director was present during the flood and was able to verify the flood extent through personal experience, photographs, air photography, and coincident high-water-mark surveying. The flood-extent maps were checked and corrected as needed by each community. Corrections from the local community were minimal or none for all seven communities with high resolution DEM data of 3 m or less (table 1). If there were flood-extent corrections made by these communities, the corrections were likely due to local temporary flood-protection efforts, such as sandbagging. Comparison of the modeled flood-extent maps with aerial photographs taken around the peak of the flood were an additional way to confirm the accuracy of the modeled inundated areas.
Standard USGS methods were used to measure flood-peak water-surface profiles from the high-water mark elevations and locations. Flood profiles were produced by plotting high-water-mark elevations by mile of stream as measured on the centerline for the flooded area from the base of the reach. The water surface between high-water marks was estimated by linear interpolation. Additional location information was added to the plot, such as the locations of street crossings or dams.
Figure 4. Example Photographs of high-water marks in August 2008.
|A. Reedsburg high-water mark 2, mudline on electrical box of sewage pump station, corroborated with city of Reedsburg mark surveyed in June during high water.
||B. Jefferson high-water mark 41, corroborated with water-stain/mud lines on nearby step, light pole, and previously surveyed high-water marks by Jefferson County during the June flood.
Table 1. Nine communities in southern Wisconsin along four major streams where high-water marks were flagged and flood-peak inundation maps and flood profiles were generated for the June 2008 flood.
[See figure 3 for location of communities. Abbreviations: USGS, U.S. Geological Survey; NWS, National Weather Service; DEM, digital-elevation model]
gage or NWS
site ID in or
|Number of high-water marks
|Located by USGS in August 2008
||Rock River and Lake Koshkonong